- #1

DunWorry

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## Homework Statement

A sphere rolls from rest down a slope without slipping. Show using energy considerations that the speed of the sphere once it reaches the bottom is V = [itex]\sqrt{\frac{10gh}{7}}[/itex]

## Homework Equations

mgh = [itex]\frac{1}{2}[/itex]mv[itex]^{2}[/itex] + [itex]\frac{1}{2}[/itex]Iw[itex]^{2}[/itex]

## The Attempt at a Solution

So I managed to do the question, but I did it using energy conservation as shown above. However I was confused as I thought if it rolls without slipping, then friction must be present. If friction is present then the energy conservation should be E[itex]_{Initial}[/itex] = E[itex]_{final}[/itex] + work done by friction. I.e the mechanical energy is not conserved

So shouldn't the equation I used above be mgh = [itex]\frac{1}{2}[/itex]mv[itex]^{2}[/itex] + [itex]\frac{1}{2}[/itex]Iw[itex]^{2}[/itex] + work done by friction?